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 A139005 Primes p such that there exist primes p'
 8389, 18433, 25253, 31231, 33647, 40289, 40357, 47237, 47303, 48731, 51721, 55621, 57331, 58763, 61129, 62303, 63601, 64189, 65657, 65677, 65983, 67723, 68491, 70099, 70571, 71341, 71741, 72739, 75653, 77153, 77641, 78509, 78511, 81401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Obviously, 2 and 5 cannot be part of such a 5-tuple. Apart from 3, all the elements of the quintuple must have the same residue mod 3, thus they are all = 1 or = -1 mod 6. Two curious facts can be observed: for p=51721 and p=63601, there are two possibilities for (p',p",p"',p""), which differ in both cases only in p"": [p=51721, p""=44371 or 44683, p"'=22531, p"=12703, p'=8101], resp. [63601, 26893 or 61417, 25939, 61, 7]. Secondly, the two quintuples for p=51721 are followed by a quintuple whose sum is one of smallest possible, only roughly half that of the two preceding solutions. LINKS Table of n, a(n) for n=1..34. Project Euler, Problem 60: Prime pair sets EXAMPLE The second such 5-tuple is [18433, 12409, 2341, 1237, 7]. The two quintuplets [51721, 44371, 22531, 12703, 8101] /*sum=139427*/ and [51721, 44683, 22531, 12703, 8101] /*sum=139739*/ are followed by [55621, 18493, 991, 883, 733] /*sum=76721*/. The next "degenerate" case is [63601, 26893, 25939, 61, 7] /*sum=116501*/ and [63601, 61417, 25939, 61, 7] /*sum=151025*/. The third "degenerate" case is [71341, 63277, 54583, 7741, 241] /*sum=197183*/ and [71341, 63277, 54583, 36187, 241] /*sum=225629*/. PROG (PARI) /* available from the author upon solving "Problem 60" on ProjectEuler.net */ CROSSREFS Sequence in context: A069402 A202588 A337959 * A252087 A253836 A253843 Adjacent sequences: A139002 A139003 A139004 * A139006 A139007 A139008 KEYWORD nonn,base AUTHOR M. F. Hasler, Apr 30 2008 STATUS approved

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Last modified August 15 04:20 EDT 2024. Contains 375172 sequences. (Running on oeis4.)